A Consider an experiment the events A and B and probabilitie

A. Consider an experiment, the events A and B, and probabilities P(A) = 0.55, P(B) = 0.45, and P(A? B) = 0.15.

Fill in the blanks.

1. The probability of A or B occuring is .
2. The probability of A and B occuring is .
3. The probability of just A occuring is .
4. The probability of just A or just Boccuring is .

Suppose 14 carpenters report to the union hall hoping for a chance to work. Three of the 14 do not have their union cards, and 6 carpenters will be selected at random for construction jobs.

Fill in the blank. (Give your answer to four decimal places.)

The probability that all 6 carpenters selected will have their union cards is .


C.

Technology and the Internet. Tablet computers have become very popular and fill a gap between smartphones and PCs. A recent survey indicated that of those people who own tablets, 72% use the device to play games and 44% use the device to access bank accounts. Suppose 30% do both -- play games and access bank accounts -- and suppose a tablet user is selected at random.

Suppose a reported case is selected at random.

Give all of your answers in decimal form.

(a) What is the probability that the tablet user plays games or accesses bank accounts?

P(G?B) =

(b) What is the probability that the tablet user does not play
games nor access bank accounts

P[(G?B)?] =

(c) What is the probability that the tablet user only plays games?

P(Only G) =

(d) What is the probability that the tablet user only accesses bank accounts?

P(Only B) =

?

B.

Suppose 14 carpenters report to the union hall hoping for a chance to work. Three of the 14 do not have their union cards, and 6 carpenters will be selected at random for construction jobs. Fill in the blank. (Give your answer to four decimal places.) The probability that all 6 carpenters selected will have their union cards is . C. 6. Consider an experiment and three events A, B, and C defined in the Venn diagram. The probability of each outcome is given. Fill in the blanks. P(B) = (Give your answer to two decimal places.) P(A? B) = (Give your answer to two decimal places.) P(B|C) = (Give your answer to four decimal places.) P(A|B\') = (Give your answer to four decimal places.) P(4|B) = (Give your answer to four decimal places.) Technology and the Internet. Tablet computers have become very popular and fill a gap between smartphones and PCs. A recent survey indicated that of those people who own tablets, 72% use the device to play games and 44% use the device to access bank accounts. Suppose 30% do both -- play games and access bank accounts -- and suppose a tablet user is selected at random. Suppose a reported case is selected at random. Give all of your answers in decimal form. (a) What is the probability that the tablet user plays games or accesses bank accounts? P(G?B) = (b) What is the probability that the tablet user does not play games nor access bank accounts P[(G?B)?] = (c) What is the probability that the tablet user only plays games? P(Only G) = (d) What is the probability that the tablet user only accesses bank accounts? P(Only B) = ?

Solution

A.

1.

P(A U B) = P(A) + P(B) - P(A n B)

= 0.55 + 0.45 - 0.15

= 0.85 [answer]

2.

P(A n B) = 0.15 [answer], as given.

3.

P(A only) = P(A) - P(A n B) = 0.55-0.15 = 0.4 [answer]

4.

P(A only or B only) = [P(A) - P(A n B)] + [P(B) - P(A n B)]

= [0.55-0.15] + [0.45-0.15]

= 0.7 [answer]

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